Cubic EquationYou are currentlybrowsing as guest. Click here to log in 

The next stage up from the quadratic equation, the general cubic equation has the form $ax^3+bx^2+cx+d=0.$
Just as there is a solution to the quadratic equation, a general solution to the cubic was found by Tartaglia and Ferro.
The problem is, even when there are three real solutions, the intermediate calculations use the roots of negative numbers, and this led directly to the acceptance of the complex numbers.
In practice, numerical solutions are found rather than using a closed form formula. Newton's Method is an efficient way to find solutions, although one must be aware that the basins of attraction have fractal boundaries.
Also related: quartic equation
Now substitute $t=u\frac{p}{3u}$ and multiply by $u^3$ to get
The Wikipedia and MathWorld articles have more information.
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